Admirers of Boris Johnson frequently pay tribute to – and his detractors just as often lament – the fact that, when it comes to the current mayor of London, the usual rules of politics do not seem to apply. So probably only Johnson could have agreed to give an interview on The Andrew Marr Show to promote a documentary with which he had co-operated, and then end up both fluffing the interview and trashing the film, Boris Johnson: The Irrepressible Rise, which is screened tonight at 9pm on BBC2.

It is also hard to imagine another politician who, after becoming the subject of a one-hour profile, would be trumped within 24 hours by his sister fronting a doc of her own: How to Be a Lady: an Elegant History presented by Rachel Johnson (BBC4, 9pm, Tuesday.)

Even by the standards of a notably media-keen family, this marks a high level of exposure, and seems to confirm Boris's confession to reporter Michael Cockerell in tonight's documentary that he and his siblings are fiercely competitive with each other. Boris Johnson: The Irrepressible Rise opens with shots of the four Johnson children playing tennis.

This week's documentary double Johnson-vision, preceded by Boris's disastrous Sunday morning appearance, surely raises the eventual prospect of an entire network dedicated to the clan. If you can have a station called Dave, then why not one called Johnson? Boris's and Rachel's dad, Stanley, is a man not known to shrink from cameras and could easily fill any stretch of the schedules that his children were unable to fill.

Revealingly, although the Boris and Rachel documentaries were independently made, a viewer of both notes elements already of a house – or home – style. The haystack hairdos shared by the central characters can be attributed to genetics, but the overlap between the programmes goes far beyond this.

The inevitably limited grammar of factual television might explain why Boris and Rachel are both filmed driving a car while checking in the rear-view mirror. But it surely goes beyond coincidence that each Johnson doc contains a sequence in which the subject complains about genital chafing: Boris while discussing the photo op in which he became stuck while riding down a zip-wire and Rachel while explaining, in her history of feminine etiquette, how female side-saddle riding developed because of the discomfort of sitting with a leg either side of the steed in pre-underwear days.

Another more pleasant link between the films is that they offer joint testimony to the benefits of high-class film research. As has become common in Cockerell's profiles of politicians, the illustrative material is notably well sourced, including home movies, footage of Boris as president of the Oxford Union, a previously unbroadcast 2004 interview with David Cameron about Johnson's sacking from Michael Howard's shadow cabinet, and a sequence in which the then Europe correspondent of the Daily Telegraph expresses Europhobic sentiments in French to a crew from Paris.

His sister's film is also distinguished by fine archive; most notably some black-and-white footage of well-born young ladies being taught at deportment classes how to get out of a car, then a new-fangled invention, without exposing themselves. There is also smart use of TV period drama, including Pride and Prejudice, to show how literature shaped the understanding of acceptable female behaviour.

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Most treacherous to Boris's presumed ambitions, though, is the moment when the film about him tackles the politician's history of behaviour towards women. Cockerell once asked the elderly Roy Jenkins about rumours of his having been a womaniser when in power, and so was never likely to skirt the gossip about a subject who was once unfortunately filmed by a camera crew having apparently been locked out of his house by his wife.

Lacking any women who will go on the record, Cockerell relies on flashing up images of tabloid headlines, and is flusteredly rebutted when he confronts Boris with the stuff: "I won't, if it's OK for you, discuss things that are done and dusted … which very largely concern my private life."

However, the presence of the questions serves to warn Johnson of a potential problem if he seeks power beyond London. The fact that Eddie Mair also pressed the mayor on the adultery allegations in the Cockerell film suggests the BBC has decided that this politician's private life is not off-limits. Johnson's media handlers are going to have a lot to handle.

And, in that respect, perhaps the most significant overlap between this week's twinned films from Johnson-vision is the only person who appears in both films – Rachel. Although the Cockerell documentary broadly belongs to the US-invented genre of "campaign biography" – a profile screened just before a politician gains a party nomination or high office – the shape and nature of the film reveals a serious weakness in BoJo's hopes of higher electability, even beyond the reservations expressed by some of the witnesses. His relatives are a huge potential liability.

Among recent British prime ministers, Margaret Thatcher had a sister and Tony Blair and David Cameron a brother, none of whom ever spoke in public, despite frequent media entreaties. Only Terry Major-Ball, John Major's eccentric elder sibling, never came close to causing the sort of distractions that Presidents Carter and Clinton suffered from their troublesome brothers Billy and Roger respectively.

Boris Johnson, though, has at least two potential Major-Balls in Rachel and Stanley. Each of them, in Cockerell's film, goes much further on the question of whether the most famous member wants to be prime minister than currently seems politic. The quantity of repeats on TV is a common complaint, but no viewer will moan more loudly than BoJo and his handlers if Cockerell's profile is repeated just after his hat, as seems inevitable, lands in the prime ministerial ring. The Johnsons' fondness for being on the box has the potential to put Boris out of the picture he is most desperate to be in.

Mark Lawson: Broadcasters may want to attract family audiences, but documentaries that scrutinise life in private homes often make for uncomfortable, post-watershed viewing. Perhaps that is part of the appeal